Simplify the following expression and state the condition under which the simplification is valid: $n = \dfrac{z^2 - 13z + 30}{z^2 - 10z}$
Answer: First factor the expressions in the numerator and denominator. $ \dfrac{z^2 - 13z + 30}{z^2 - 10z} = \dfrac{(z - 3)(z - 10)}{(z)(z - 10)} $ Notice that the term $(z - 10)$ appears in both the numerator and denominator. Dividing both the numerator and denominator by $(z - 10)$ gives: $n = \dfrac{z - 3}{z}$ Since we divided by $(z - 10)$, $z \neq 10$. $n = \dfrac{z - 3}{z}; \space z \neq 10$